Elementary Linear Algebra
8th Edition
ISBN: 9780357156100
Author: Ron Larson
Publisher: Cengage Limited
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Chapter 7.2, Problem 46E
Guide Proof Prove nonzero nilpotent matrices are not diagonalizable
Getting started: From Exercises 80 in Section 7.1, you know that 0 is the only eigenvalue of the nilpotent matrix A. Show that it is impossible for A to be diagonalizable.
(i) Assume A is diagonalizable, so there exists an invertible matrix P such that
(ii) Find A in term of
(iii) Find a contradiction and conclude that nonzero nilpotent matrices are not diagonalizable.
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Chapter 7 Solutions
Elementary Linear Algebra
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